isomesh 0.1.0.dev2

Fast, robust isosurface extraction from arbitrary implicit functions using adaptive octree and Manifold Dual Contouring

isomesh

Fast, robust isosurface extraction from arbitrary implicit functions using adaptive octree and Dual Contouring.

Features

• Sharp feature preservation via QEF (Quadric Error Function) vertex placement -- corners and edges are captured exactly, not rounded like Marching Cubes
• Manifold, watertight output guaranteed for closed surfaces
• Adaptive refinement -- concentrates cells at feature boundaries, smooth regions stay coarse
• Rust core with Python bindings (PyO3 + maturin) -- zero-copy numpy array exchange
• Batch evaluation -- the user's implicit function is called with (N, 3) arrays, not point-by-point
• Newton surface projection -- all vertices lie exactly on the isosurface (machine precision)

Quick Start

import isomesh
import numpy as np

def sdf_sphere(pos: np.ndarray):
    norms = np.linalg.norm(pos, axis=1)
    values = norms - 1.0
    gradients = pos / np.linalg.norm(pos, axis=1, keepdims=True)
    return values, gradients

vertices, faces = isomesh.extract(
    func=sdf_sphere,
    bbox_min=(-2, -2, -2),
    bbox_max=(2, 2, 2),
    min_depth=4,
    max_depth=7,
    angle_threshold=30.0,   # degrees -- sharp feature detection
    iso_value=0.0,
)

# vertices: (V, 3) float64 -- all on the isosurface
# faces: (F, 3) int64 -- consistently oriented triangles

Installation

Requires Python >= 3.11 and a Rust toolchain.

pip install maturin
git clone <repo-url> && cd isomesh
maturin develop --release

How It Works

isomesh uses Dual Contouring on an adaptive octree:

1. Adaptive octree construction -- uniform grid at min_depth, then feature-sensitive refinement to max_depth based on normal angle spread and gradient variation
2. QEF vertex placement -- one vertex per cell via Jacobi SVD eigendecomposition with mass-point bias for rank-deficient cases
3. Newton surface projection -- one Newton step projects each vertex exactly onto the zero-isosurface
4. Quad generation -- canonical-edge iteration with flatness-based triangulation
5. All surface leaves forced to max_depth -- eliminates T-junction holes, guarantees watertight output

Function Interface

The implicit function must be vectorized:

def f(positions: np.ndarray) -> tuple[np.ndarray, np.ndarray | None]:
    """
    Args:
        positions: (N, 3) float64 array of query points
    Returns:
        values: (N,) float64 -- implicit function values
        gradients: (N, 3) float64 or None -- if None, estimated via finite differences
    """

Dual Contouring vs Marching Cubes

Comprehensive comparison across 10 benchmark shapes using isomesh (Dual Contouring) and PyMCubes (Marching Cubes) at equivalent resolution (depth 6 = 64 cells/axis).

Summary

Metric	MC (res=65)	DC Uniform (d=6)	DC Adaptive (4->6)	DC Adaptive (4->7)
Manifold	10/10	10/10	10/10	10/10
Watertight	10/10	10/10	10/10	10/10
Total vertices	81,112	80,693	72,629	270,770
Total time	0.75s	7.69s	6.86s	15.25s
Avg SDF error	3.10e-04	5.74e-05	5.75e-05	2.17e-05
Avg min angle	34.7	39.8	39.6	40.0

Surface Accuracy

Newton projection places DC vertices nearly exactly on the isosurface:

| Shape | MC mean |SDF| | DC mean |SDF| | Improvement | |-------|:-------:|:-------:|:----------:| | sphere | 9.63e-05 | 1.21e-18 | ~10^13x | | thin_shell_hemi | 6.86e-05 | 1.17e-11 | ~10^6x | | chamfered_sphere | 2.58e-04 | 5.12e-07 | ~500x | | mechanical_part | 3.25e-04 | 4.05e-05 | ~8x | | bunny | 4.38e-04 | 4.38e-04 | ~1x | | simjeb_148 | 1.35e-03 | 8.95e-05 | ~15x |

Triangle Quality

DC consistently produces better-shaped triangles (higher minimum angle = less degenerate):

Shape	MC min angle (avg)	DC min angle (avg)
sphere	31.6	43.7
thin_shell_hemi	31.4	43.1
chamfered_sphere	35.5	43.4
box	44.1	44.5
mechanical_part	40.3	41.0
bunny	32.3	30.9
simjeb_148	34.6	33.2

Sharp Feature Comparison

DC (Dual Contouring) preserves sharp edges and corners via QEF vertex placement. MC (Marching Cubes) rounds them by linear interpolation.

Thin Feature & Complex Geometry

Adaptive Refinement

Adaptive mode concentrates resolution where needed:

Shape	Adaptive (4->6) V	Uniform (d=6) V	Ratio
sphere	536	8,600	16x fewer
chamfered_sphere	7,064	7,064	1x
cylinder	4,328	4,328	1x

For smooth shapes like sphere, adaptive refinement skips unnecessary subdivision, reducing vertex count by 16x with comparable accuracy.

Usage with Neural SDF Models

isomesh is designed for extracting meshes from SDF-based 3D generative models (e.g., DeepSDF, SDF-Diffusion) trained on mechanical parts like SimJEB.

Recommended Configuration

import isomesh
import numpy as np
import torch

def make_sdf_func(model, device='cuda'):
    """Wrap a neural SDF model for isomesh.

    Always provide autodiff gradients -- finite difference gradients
    are unreliable on neural SDFs.
    """
    @torch.no_grad()
    def func(points: np.ndarray):
        pts = torch.from_numpy(points).float().to(device)
        pts.requires_grad_(True)

        with torch.enable_grad():
            values = model(pts)            # (N,)
            grads = torch.autograd.grad(
                values.sum(), pts, create_graph=False
            )[0]                           # (N, 3)

        return values.cpu().numpy(), grads.cpu().numpy()
    return func

vertices, faces = isomesh.extract(
    make_sdf_func(model),
    bbox_min=(-1.0, -1.0, -1.0),
    bbox_max=(1.0, 1.0, 1.0),
    min_depth=4,            # 16³ base grid
    max_depth=7,            # 128³ effective resolution
    adaptive=True,          # essential for mechanical parts
    angle_threshold=30.0,   # detects 90° edges reliably
    iso_value=0.0,
)

Why These Settings

Parameter	Value	Rationale
adaptive	True	Mechanical parts have large flat surfaces + sharp edges/holes. Adaptive refinement concentrates resolution at feature boundaries, keeping flat regions coarse.
min_depth	4	16³ = 4,096 initial corners -- a good first GPU batch. Lower risks missing thin features at the base grid; higher diminishes the benefit of adaptive refinement.
max_depth	7	128³ effective resolution captures fillets, hole edges, and fine details.
angle_threshold	30.0	Mechanical edges are typically 90°, well above this threshold. Lowering it risks false-positive refinement from noisy neural gradients on flat surfaces.

Quality Presets

# Batch generation (speed-oriented, hundreds of shapes)
min_depth=4, max_depth=7, adaptive=True

# Single shape, final output (quality-oriented)
min_depth=5, max_depth=8, adaptive=True

Tips

• Always provide autodiff gradients. Neural SDF + finite differences = poor accuracy. The wrapper above uses torch.autograd.grad to get exact gradients while keeping the outer scope in no_grad mode.
• Don't lower angle_threshold below 25°. Neural gradients are noisier than analytic ones. A lower threshold causes over-refinement on surfaces that are actually flat.
• Thin features are handled automatically. The Lipschitz guard detects thin walls even in cells without sign changes.
• Output is manifold and watertight. Manifold Dual Contouring guarantees this -- no post-processing needed for downstream simulation or 3D printing.
• QEF preserves sharp edges exactly. Unlike Marching Cubes, which places vertices on grid edges (chamfering corners), QEF vertex placement captures true edge and corner geometry.

API Reference

isomesh.extract(
    func,                    # vectorized SDF: (N,3) -> ((N,), (N,3)|None)
    *,
    bbox_min=(-1, -1, -1),   # bounding box (expanded to cube if non-cubic)
    bbox_max=(1, 1, 1),
    min_depth=3,             # uniform base resolution (2^min_depth cells/axis)
    max_depth=7,             # max adaptive refinement depth
    angle_threshold=30.0,    # degrees -- feature detection sensitivity
    iso_value=0.0,           # isosurface level
    fd_step=1e-5,            # finite difference step (if gradients not provided)
    adaptive=False,          # enable adaptive refinement
) -> (vertices, faces)

Architecture

src/                        # Rust core
  lib.rs                    # PyO3 module entry
  bbox.rs                   # Bounding box, expand-to-cubic
  octree/                   # Adaptive octree
    build.rs                # Construction + feature-sensitive refinement
    cell.rs, types.rs       # Data structures
    morton.rs               # Morton code spatial indexing
  eval/                     # Function evaluation bridge
    bridge.rs               # Batch Python<->Rust with GIL management
    cache.rs                # Corner value/gradient cache
  dc/extract.rs             # Dual Contouring mesh extraction
  qef/quadric.rs            # QEF solver (Jacobi SVD, mass-point bias)
  util/math.rs              # 3x3 eigendecomposition

python/isomesh/             # Python API
  _core.py                  # extract() wrapper + validation
  _validation.py            # Input checking with clear error messages

Testing

maturin develop --release
pytest tests/ -v

Benchmarks

The benchmark suite compares isomesh against PyMCubes across 10 shapes in 4 categories:

Category	Shapes	What it tests
Basic	Sphere, Torus	Smooth surfaces, analytic ground truth
Sharp features	Box, Rotated box, Chamfered sphere, Cylinder, Mechanical part	Sharp edges, corners, non-axis-aligned edges, CSG operations
Thin features	Hemisphere shell (wall=0.08)	Thin walls, open boundaries
Complex geometry	Bunny, SimJEB 148 (mesh-based SDF)	Real CAD parts, complex topology

# Full benchmark (all shapes, all methods, with rendering)
uv run python benchmarks/run_benchmark.py

# Selective
uv run python benchmarks/run_benchmark.py --shapes sphere box chamfered_sphere
uv run python benchmarks/run_benchmark.py --methods uniform adaptive
uv run python benchmarks/run_benchmark.py --no-render --no-stl

References

• Ju, Losasso, Schaefer, Warren. "Dual Contouring of Hermite Data." SIGGRAPH 2002.
• Schaefer, Ju, Warren. "Manifold Dual Contouring." IEEE TVCG 13(3), 2007.
• Garland, Heckbert. "Surface Simplification Using Quadric Error Metrics." SIGGRAPH 1997.
• Lindstrom. "Out-of-Core Simplification of Large Polygonal Models." SIGGRAPH 2000.

License

MIT